My wife used my credit card in her business and used 20,000 (AMEX CARD) and then she couldn’t pay off the debt, now it’s hurting my credit and we wanted to move the debt from me to her, taking in consideration that I admit that I allowed her to use the card and she admit that she used it on her business.
we wanted to move the debt from me to her
The only way to get rid of a specific credit card's debt is to pay it off. Having her take out a loan and using that money to pay the card effectively transfers the debt from your card to hers.
According to here, some credit cards allow you to transfer balances between authorized users/joint account holders. However, American Express is not one of them.
You could try transferring the balance to a credit card that does; preferably one that gives you a 0% interest rate on balance transfers for 12 to 18 months.